TY - JOUR

T1 - Clustering in Euler-Euler and Euler-Lagrange simulations of unbounded homogeneous particle-laden shear

AU - Kasbaoui, M. Houssem

AU - Koch, Donald L.

AU - Desjardins, Olivier

N1 - Funding Information:
This work was supported by NSF grants CBET-1233793 and CBET-1505759.
Publisher Copyright:
© 2018 Cambridge University Press.

PY - 2019/1/25

Y1 - 2019/1/25

N2 - Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh-Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler-Lagrange formalism are compared to Euler-Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.

AB - Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh-Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler-Lagrange formalism are compared to Euler-Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.

KW - instability

KW - multiphase and particle-laden flows

KW - multiphase flow

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U2 - 10.1017/jfm.2018.796

DO - 10.1017/jfm.2018.796

M3 - Article

AN - SCOPUS:85057136466

SN - 0022-1120

VL - 859

SP - 174

EP - 203

JO - journal of fluid mechanics

JF - journal of fluid mechanics

ER -